Recovering Three-Dimensional Surfaces with Multi-images Shape-From-Shading Method

Abstract

Three-dimensional (3-D) shape reconstruction is one of the fundamental problems in the field of computer version. Most existing shape-from-shading (SFS) methods are based on signal image and orthogonal projection. But the reflectance map equation is a nonlinear partial differential equation about two random variables. So the SFS is an ill-posed problem. Further more, orthogonal projection used to simulate the imaging processes of camera is not very accurate. This paper proposes a new SFS method under perspective projection with multi-images. Three images with different lighting source directions are captured by camera firstly. Following three reflectance map equations which are described by Lambertain model are established. Then the gradient vectors of the 3-D surface are calculated by solving the reflectance map equations. The gray constraint and gradient component constraint conditions are used to construct target function, and the corresponding Eulor-Poision equations are derived. Simultaneously, discrete difference is used to approximate differential operation. New iterative 3-D shape reconstruction algorithm is proposed by the discrete difference equation. Three pixel values are used to solve certain gradient value in our method. So the ill-posed problem in traditional SFS which solves a single reflectance map equation can be avoided. At last, experimental results of 3-D reconstruction show that the proposed method is effective.